Not exactly....
If I take a 4x4x4 lump of steel and heat it up to a temperature that is say, 100* above the ambient, it's going to require X amount of time at Y amount of BTU's to do so.
Now you let it sit and return to ambient. Start a watch and data log the time it takes.
Repeat the exact same test on a lump that is 3X, then 2X, and 1X. Guess what? as it gets smaller it takes less time to heat it up and less time for it to cool off. The point here is barrel mass plays into this. So, a fluted barrel will heat up faster because you pulled mass from it. It has to. It will also cool quicker because there's less mass holding onto the heat.
The idea that flutes increase surface area and accelerate the convection is nice to think about, but in practice, it makes almost no difference. If we use any air-cooled engine as the example we see that the cylinders are designed with very thin airfoils that expose a tremendous amount of surface area by comparison. Your fluted barrel is nowhere near that efficient. -Like not even on the same continent of that efficiency.
Now complicate the whole thought process by the fact that roughly 50% of the circumference is shrouded/blanketed by the rifle stock forend precisely where almost all of the heat is generated.
Again, treat it for what it is: Looks cool and reduces some weight.
C.